Physical therapists provide instructions for gradual muscle strengthening via different-colored, wide elastic bands. These are also available for inexpensive purchase at sports stores. It is important to use careful, smooth, and slow motions with these so as not to injure joints.
For those who can manage to increase their program time and endurance to include this type of exercise, weight training or other resistance exercise affords many benefits. There are general health-building mechanisms of resistance exercise--increased muscle strength can protect vulnerable joints and the lower back, and it can slow the loss of bone that occurs in osteoporosis.
Most strength exercises involve lifting or pushing a weight against gravity, and repeating that movement a number of times (repetitions or "reps"). The amount of weight and the number of reps determine how much effort is being put forth in the exercise. You should breathe out during the main effort of the lift (or push), and breathe in during the return movement. Slow movements are better than fast - e.g., 3 seconds for the lift/exhale, 1-second hold, and 3 seconds for the lower/exhale. Pause between each rep to increase tolerance.
Participants can do resistance training two or more days a week, but they should not exercise the same muscle group on any two days in a row. One day a week of resistance training may have just as much value and may be more protective of the body than working out a greater number of times, and this is probably much more feasible for those with FM.
As with all exercise, warm-ups and cool-downs are important.